Spect gamma camera

ABSTRACT

A method and apparatus of obtaining and reconstructing an image of a portion of a body, administered by a radiopharmaceutical substance, by using Single-photon emission computerized tomography (SPECT) for determination of functional information thereon. The method comprises (a) acquiring gamma ray photons emitted from said portion by means of a detector capable of converting the photons into electric signals, the detector having at least one crystal and allowing said gamma rays having incident angles essentially exceeding 5 degrees and, preferably, exceeding 10 degrees to be detected; (b) processing said electric signals by a position logic circuitry and thereby transforming them into data indicative of positions on said photon detector crystal, where the photons have impinged the detector; and (c) reconstructing an image of a spatial distribution of the pharmaceutical substance within the portion of the body by processing said data and taking into consideration weight values which are functions of angles and, possibly, distances between different elements of the portion of the body and corresponding elements of this position&#39;s projection on the detector.

FIELD OF THE INVENTION

[0001] This invention relates to Nuclear Medicine, and, moreparticularly, to Single-photon emission computerized tomography (SPECT)imaging technique.

BACKGROUND OF THE INVENTION

[0002] SPECT is one of Nuclear Medicine imaging techniques that enableto acquire functional information about patient's specific organ or bodysystem. This functional information is attained from analysis ofinternal radiation obtained from pharmaceutical substance administeredto the patient, which is labeled with a radioactive isotope. Theradioactive isotope decays, resulting in the emission of gamma rays,thus providing with information on the concentration of theradiopharmaceutical substance introduced to the patient's body. Aninstrument for the detection of gamma ray emissions of theradiopharmaceutical substance administered in the body is known as gammacamera. The SPECT technique collects gamma ray photons that are emittedfrom the patient and reconstructs an image or a series of images of theplace in the body from which the gamma rays are originated. From thispicture a physician can determine how a particular organ or system isfunctioning. The main components making up a conventional gamma cameraare a collimator for passing therethrough gamma rays to be detected,photon detector crystal or detector array, position logic circuits anddata analysis computer. Depending on the type of the detector crystal,conventional gamma camera may or may not include a photo-multiplier tubearray.

[0003] A gamma ray photon that has passed through the collimators,interacts with the detector crystal by means of the Photoelectric Effector Compton Scattering with ions of the crystal. These interactions causethe release of electrons which in turn interact with the crystal latticeto produce light, in a process known as scintillation. Since only a verysmall amount of the light is given off from the crystal,photo-multiplier tubes are normally attached to the back of the crystal.Typically, such conventional gamma camera has several photo-multipliertubes arranged in a geometrical array. The position logic circuits thatfollow the photo-multiplier tube array, receive the electrical impulsesfrom the tubes and determine where each scintillation event occurred inthe detector crystal. Finally, in order to deal with the incomingprojection data and to process it into a readable image of the spatialdistribution of activity within the patient, a processing computer isused. The computer may use various different methods to reconstruct animage.

[0004] Different collimators are used in gamma cameras to limit thedetection of photons to incidence range of predetermined angles. Aparallel-hole collimator is usually made from lead or tungsten and hasthousands of straight parallel holes in it, allowing only those gammarays traveling along certain directions to reach the detector. As aresult of that, the ratio of emitted, versus detected, photons may reach10000 to 1. In order to decrease this ratio, converging or diverginghole collimators, for example, fan-beam and cone-beam are also known inthe art. The usage of these collimators increases the number of photoncounts, which improves sensitivity. The sensitivity, however, isinversely related to geometric resolution, which means that improvingcollimator resolution decreases collimator sensitivity, and vice versa.

[0005] The current use of collimators results in a rather low detectionefficiency of conventional SPECT which leads to prolonged dataacquisition time and the need to administer high dosage of theradiopharmaceutical substance.

SUMMURY OF THE INVENTION

[0006] The general object of the present invention, which will bedescribed subsequently in greater detail, is to provide a noveltechnique for acquisition and reconstruction of SPECT images obtained bya gamma camera.

[0007] The technique of the present invention enables the gamma camerato accept gamma rays at the incident angles in the range of up to 90degrees, e.g. to work when the gamma rays are non-collimated, whilst inthe conventional way of acquisition and reconstruction of SPECT images,gamma rays having incident angles exceeding 2-4 degrees are normally notdetected.

[0008] The present invention is based on a correct account of thedirections of the gamma rays, achieved by taking into considerationweight values which establish coupling between different parts of theexamined organ and the corresponding parts of the organ's projection onthe detector. For example, the weight values might be chosen as afunction of angles at which each element of the detector is viewed fromdifferent points of the corresponding imaged area of the organ.

[0009] There is provided in accordance with the present invention, amethod of obtaining and reconstructing an image of a portion of a body,administered by a radiopharmaceutical substance, by using SPECT fordetermination of functional information thereon, comprising the stepsof:

[0010] (a) acquiring gamma ray photons emitted from said portion bymeans of a detector capable of converting the photons into electricsignals, the detector having at least one crystal and allowing saidgamma rays having incident angles essentially exceeding 5 degrees and,preferably, exceeding 10 degrees to be detected;

[0011] (b) processing said electric signals by a position logiccircuitry and thereby transforming them into data indicative ofpositions on said photon detector crystal, where the photons haveimpinged the detector; and

[0012] (c) reconstructing an image of a spatial distribution of thepharmaceutical substance within the portion of the body by processingsaid data and taking into consideration weight values which arefunctions of angles and, possibly, distances between different elementsof the portion of the body and corresponding elements of this position'sprojection on the detector.

[0013] The technique of the present invention may lead to substantialimprovement in image resolution (better than 7 mm) and improvement inimage sensitivity with respect to the conventional SPECT technique. Thatmay result in better lesion detectability, shorter acquisition time andadministration of smaller doses of radiopharmaceutical substances to thepatient.

BRIEF DESCRIPTION OF THE DRAWING

[0014] In order to understand the invention, its operating advantagesand to see how it may be carried out in practice, preferred embodimentswill now be described, by way of a non-limiting examples only, withreference to the accompanying drawings, in which:

[0015]FIG. 1 is a pictorial illustration of the operation of a gammacamera in accordance with the present invention.

[0016]FIG. 2a is a simplified diagram depicting one example of thecoupling between different elements of the detector and correspondingelements of the body in accordance with the present invention;

[0017]FIG. 2b is a simplified diagram depicting another example of thecoupling between different elements of the detector and correspondingelements of the body in accordance with the present invention; and

[0018]FIG. 3 is a pictorial illustration of an alternative embodiment ofa gamma camera according to the present invention.

[0019]FIG. 4a illustrates a portion of a collimator to be used in apreferred embodiment of a gamma camera in accordance with the presentinvention, having hexagonal holes arranged in a beehive arrangement.

[0020]FIG. 4b illustrates a front-view of a portion of a collimator tobe used in another preferred embodiment of a gamma camera in accordancewith the present invention, having circular holes arranged in a beehivearrangement, and separating septa.

[0021]FIG. 4c illustrates an alternative collimator hole having ovalshape.

DETAILED DESCRIPTION OF EMBODIMENTS

[0022] Reference first is made to FIG. 1 depicting a side view of asimplified schematic diagram of gamma camera in accordance with thepresent invention, for obtaining a SPECT image of a portion of a bodythat has been administered by a radiopharmaceutical substance whichradiates gamma rays.

[0023] The gamma camera 1 comprises a detector 2 mounted above aninspected portion 4 of a body 5, a position logic circuitry 7 and a dataanalysis computer 8, all connected appropriately.

[0024] Detector 2 includes at least one photon detector crystal 6 facingthe portion 4 of body 5. The photon detector crystal 6 may be in theform of a semiconductor crystal or crystals. This crystal(s) may beselected from a first group including Cadmium-Telluride (CdTe),Cadmium-Zinc-Telluride (CeZnTe), Lead Iodine (PbI).

[0025] The detector 2 of the gamma camera 1 may further include at leastone photo-multiplier 9. The photon detector crystal(s) in this case maybe selected from a second group including Sodium Iodine (NaI), BismuthGermanate (BGO), Yttrium Oxyorthosilicate (YSO), Cerium-doped LutetiumOxyorthosilicate (LSO) and Cesium-Iodine (CsI) with solid statephoto-diode or avalanche photo-diode (APD).

[0026] The detector crystals listed above have different characteristicsthat are relevant for SPECT imaging: they differ in their ability toresolve photon energy (also termed “energy resolution”), their internalspatial resolution and their stopping power. All of thesecharacteristics affect the resolution and sensitivity of the resultantimages. Therefore, SPECT cameras utilizing different detector crystalswill yield different resolution, using the same reconstructionalgorithm.

[0027] Detector 2 may also be in the form of an array of photon detectorcrystals arranged in at least one row. The photon detector crystal arraymay be in the form of a plane or a ring surrounding the portion of thebody. For example, detector 2 may be of the kind used in a known per seAnger camera.

[0028] Detector 2 may be capable of rotating around, or moving along, adesired trajectory relative to the body to acquire data at multiplepredetermined positions from multiple views around the body.

[0029] Angles of incidence of gamma rays from the portion 4 of the body5 may be in the range from 0° to 90°. Detector 2 may be provided withmeans 10 establishing angles of incidence of gamma rays on the detectorin a restricted range. It is noted that by angle of incidence it ismeant the angle between the perpendicular to the surface of the detectorand the ray path.

[0030] Such means may be in the form of appropriate collimators.However, these means should be such as to allow the gamma rays havingvarious incident angles in the range of 0 to 5 or more degrees, andpreferably, in the range of 0 to 10 or more degrees, to be detected. Thecollimator holes may be symmetric, such as circular or hexagonal shapedholes, or have different dimensions along the different axis, such asellipse or rectangular shape holes. Furthermore, the shape of the boreof the collimators may be cylindrical, conic or other converging shapes.

[0031] Alternatively, when no collimators are used, rows or columns ofsepta may be used for limiting the number of beams impinging thedetector, to beams coming from certain directions. For limiting thefield of view of the entire detector 2, at least one septum 11 may bemounted at detector 2 along one of its axes (FIG. 3), however it isrecommended to use at least two, mounted at opposite edges. The septaare designed to avoid the penetration of gamma rays 13 emanating fromoutside the field of view and thereby decrease a computational load.

[0032] In operation, detector 2 acquires radioisotope gamma ray photons3, which are emitted from portion 4 of body 5 and passing through means10. The gamma photons impinge the photon detector crystal 6. If thecrystal 6 is a semiconductor crystal selected from the first groupspecified above, then the crystal converts the photons into electricsignals, which are fed into a position logic circuitry 7 for processing.Alternatively, if the crystal is selected from the second groupspecified above, i.e. is of the kind that utilizing photo-multipliers,then the crystal converts photons 3 into scintillation light, which is,thereafter, transformed into electric signals by photo-multiplier 9.

[0033] As a result of the processing, the electric signals aretransformed into data indicative of photon energy and positions on thephoton detector crystal 6 in which the photons impinge the detector. Thedata that includes the position at which each photon impinged thedetector, for each position of the detector, is termed projection.Thereafter, the projections are fed into a data analysis computer 8 forthe purpose of reconstructing an image of a spatial distribution of thepharmaceutical substance within the portion of the body by processingsaid data. The photon energy information is registered for theassessment of the amount of Compton scattering that is introduced in theacquisition. In general, there is one energy window around each peak ofthe radio-pharmaceutical substance. The width of each window ispreferably set as narrow as may be reasonable to the specific detectorthat is used, in order to reject as many scattered photons as possible.

[0034] The reconstruction of the image according to the presentinvention may be performed based on any appropriate existing algorithm,however, it should necessarily be based on weight values, which arefunctions of either angles or angles and distances between differentelements of the portion of the body and corresponding elements of body'sprojection on the detector.

[0035] For example, the reconstruction of the image may start fromdividing an area of the detector facing the body onto M bins anddividing portion 4 of body 5 onto N voxels. As a result of suchdiscretization, the photons are binned according to their position onthe detectors and a set of values D_(ik) (wherein i=1, . . . ,M)indicative of a number of photons acquired by the i-th bin, for anyposition k (wherein k=1, . . . ,L) at which the detectors are positionedwhile acquiring this data, is provided. Clearly, if the detectorincludes M crystals and each crystal is associated with a bin, then thestep of additionally dividing of the detector's area onto M bins isunnecessary.

[0036] Further, a coupling between each bin of the detector at eachposition k at which the detectors are positioned while acquiring thisdata, and each voxel of the portion of the body is established. As aresult of the coupling, a matrix P={P_(ijk)} of to weight values of thevoxels of the portion of the body (wherein i=1, . . . ,M, j=1, . . . ,Nand k=1, . . . ,L) is constructed. For the rest of the discussion, thereference to the position k in the elements of the matrix P, and in thedetector values D will be omitted.

[0037]FIG. 2a shows a simplified, two dimensional diagram depicting oneexample of the coupling between bins 31 having indices i, i+1, i+2, . .. and a voxel 32 having an index j, which results in weight valuesP_(ij), P_(i+1j), and P_(i+2j) that are functions of a set of anglesα_(ij), α_(i+1j), α_(i+2j), . . . , and possibly distances between thebins 31 and voxel 32. In the case when collimators are used, a photonthat emanated from voxel i and is within the angle of view of a givenbin, may be absorbed by the walls of the collimator at that area.Therefore, the P_(ij) should be multiplied by the relative effectivearea of bin i as viewed from voxel j. (see, for example, C. E. Metz, F.B. Atkins and R. N. Beck, “The Geometric tansfer function component forscintillation camera collimators with straight parallel holes,” Phys.Med. Biol., 1980, v. 25, p. 1059-1070).

[0038] According to a more general example, P may be a matrix in whicheach of the matrix elements P_(ij) is a function of an average angle andpossibly distance at which a detector bin having an index i is viewedfrom the voxel having an index j. Alternatively, the P may be a matrixin which each of the matrix elements P_(ij) is a function of an angleand possibly distance at which the detector bin having an index i isviewed from a center of the voxel having an index j.

[0039]FIG. 2b illustrates another example, in 2 dimensions, wherein P isa matrix in which its elements are presented by equation${P_{ij} = {c\frac{{l\quad \cos \quad \Theta_{i}}\quad}{z^{2}}}},$

[0040] wherein Θ_(i) is the angle at which the detector's bin having anindex i views the voxel having an index j, c is a constant, l is thelength of the detector bin's side, z is the distance between the centersof the voxel having index j and the bin having index i. As yet anotherexample, the value of the angle Θ_(i) may be an average angle of viewfrom the bin having an index i into the voxel having an index j.

[0041] In the most general case, the three dimensional case, the weightsdepend on the solid angle between a given point in a voxel and a givendetector bin, on the position k of the detector relative to the startingpoint of the acquisition and on the distance of the voxel from the bin.As with the two-dimensional case, when collimators are used, theseweights are multiplied by the relative effective area of the binassociated with that solid angle.

[0042] The elements of the matrix P may be modified to incorporate theattenuation effect, when attenuation map is available. The modificationis such that the P_(ij) as described above, will take into account theattenuation terms that are associated with the voxels through which theray emanated at voxel j pass to arrive at bin i, when the detectors arein position k. (see, for example, D. L. Baiely, B. F. Hutton & P. J.Walker, “Improved SPECT Using Simultaneous Emission and TransmissionTomography”, J Nuc Med, 1987, 28: 844-851).

[0043] In order to derive voxel values V_(j) of an image of the portionof the body and thereby to obtain a spatial distribution of thepharmaceutical substance indicating the functional information on thisportion of the body, a mathematical model should be formulated andsolved. Formulation of the mathematical model includes modeling arelation between the set of values D_(i) and a set of unknown voxelvalues V_(j) of the image.

[0044] As one example, the mathematical problem for deriving V_(j) maybe formulated as a set of algebraic equations$D_{i} = {\sum\limits_{j = 1}^{N}\quad {P_{ij}V_{j}}}$

[0045] with respect to each unknown value V_(j) may be solved, whereinj=1, . . . , N and i=1, . . . , M. As it can be clear to a man of theart, the set of equations in a general form is:${D_{i} = {{\sum\limits_{j = 1}^{N}\quad {P_{ij}V_{j}}} + E_{i}}},$

[0046] i.e. also includes a set of measurement errors E_(i).

[0047] As another example, the mathematical problem may be formulated asan optimization problem with a likelihood function that should be solvedfor deriving the unknown values V_(j) (see, for example, the techniqueof L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction foremission tomography,” IEEE Trans Med. Imaging, 1982, v. 1, p. 113-122,or K. Lange and R. Carson, “EM reconstruction algorithm for emissiontomography,” J. Comput. Assist. Tomogr., 1984, v. 8, p. 306-316).

[0048] The optimization problem is formulated as a statistical model ofthe emission process for estimating image data. According to the model,the number of photons V_(j) that are emitted from a voxel with an indexj obeys the Poisson distribution${{P\left( {V_{j} = n} \right)} = \frac{^{- {\lambda {(V_{j})}}}{\lambda \left( V_{j} \right)}^{n}}{n!}},$

[0049] wherein P(V_(j)=n) is the probability of having n events ofphoton emissions in the j-th voxel, and λ(V_(j)) is the unknown meanvalue of the Poisson distribution. Further, the number of photons D_(i)that are acquired by the i-th bin also obeys the Poisson distributionwith mean value of the distribution λ(D_(i)). The random variables V_(j)and D_(i) as well as their respective mean values λ(V_(j)) and λ(D_(i))are, correspondingly, related via the following equations$D_{i} = {{\sum\limits_{j = 1}^{N}\quad {P_{ij}V_{j}\quad {and}\quad {\lambda \left( D_{i} \right)}}} = {\sum\limits_{j = 1}^{N}\quad {P_{ij}{{\lambda \left( V_{j} \right)}.}}}}$

[0050] Thus the optimization problem is used to estimate the mean valueλ(V_(j)) of the Poisson random variables V_(j), using the D_(i)valuesmeasured by the detector. For example, one conventional statisticalapproach for determination of V_(j) is to find a maximum of thelikelihood function${{L\left\lbrack {\lambda \left( D_{i} \right)} \right\rbrack} = {\prod\limits_{i = 1}^{M}\quad \frac{^{- {\lambda {(D_{i})}}}{\lambda \left( D_{i} \right)}^{D_{i}}}{D_{i}!}}},$

[0051] with respect to the unknowns V_(j).

[0052] An image of the portion of the body reconstructed by utilizingthe algorithms described above may be a two dimensional image or a threedimensional image of the portion of the body.

[0053] As yet another example, the mathematical problem may beformulated as a Bayesian optimization problem, in which a likelihoodfunction is utilized together with a penalty function known per se. (Seefor example, P. J. Green, Bayesian reconstruction from emissiontomography data using a modified EM algorithm, IEEE Trans Med. Imaging,1990, V. 9, p. 84-93, or P. J. Green, On the use of the EM algorithm forpenalised likelihood estimator, J. Roy. Statist. Soc. (B), 1990,52:443-452, or D. Geman and G. Reynolds, Constraint Restoration and theRecovery of Discontinuities, IEEE trans on Pattern Analysis and MachineIntelligence, 1992, v. 14, p. 367-383.) This optimization problem shouldbe solved for deriving the unknown values V_(j). As an example, but notlimited to, a general form of the Bayesian optimization problem can bewritten as follows:

V=arg max{L[λ(D _(i))]+αF(V _(j) ,V _(k))},

[0054] where α is the weight that is given to the prior function F.

[0055] For instance the penalty function may be chosen in the form of${{F\left( {V_{j},V_{k}} \right)} = {\sum\limits_{j,k}^{\quad}\quad \left( {V_{j} - V_{k}} \right)^{2}}},$

[0056] wherein the sum is taken over two neighboring voxels havingindices j and k. Such a penalty function expresses some prior knowledgeabout the smoothness characteristics of the reconstructed image. Otherpenalty functions, which preserve discontinuities are more adequate forSPECT reconstruction.

[0057] As it can be clear to, a man of the art, the choice of theoptimal minimal incidence angle utilized for a scan, is guided by thetrade-offs between resolution and sensitivity that can be tolerated.Factors, for instance, such as desired acquisition time, resolution,sensitivity, noise characteristics should also be taken into account.This choice dictates whether to use collimators, if so what are theircharacteristics, or alternatively use septa or do not use collimators atall. When using collimators for example, the characteristics of thecollimator, such as the hole dimensions, are determined by the acceptedincidence angle, as well as by other factors. The accepted incidenceangle itself is determined by the desired resolution and sensitivity.Hence, practical solutions will depend on the factors mentioned aboveand can be optimized accordingly. For example, in cardiac imaging, thecollimator characteristics are guided by the priority to have a highsensitivity image rather than high resolution one, whereas for brainperfusion images, because of the brain's fine structures, highresolution is required.

[0058]FIG. 4a illustrates a portion of a collimator to be used in apreferred embodiment of a gamma camera in accordance with the presentinvention, having hexagonal holes arranged in a beehive arrangement. Thecollimator 44, is arranged in a beehive configuration of hexagonal holes42.

[0059]FIG. 4b illustrates a portion of a collimator to be used inanother preferred embodiment of a gamma camera in accordance with thepresent invention, having circular holes arranged in a beehivearrangement, and separating septa. In this embodiment the collimatorconsists of hexagonal cells 47, each cell having a circular hole 48defined by the walls 46.

[0060]FIG. 4c illustrates an alternative collimator hole having ovalshape 50. The collimator holes may be symmetric, such as circular,square or hexagonal shaped holes. Alternatively the collimator holes maybe non-symmetric. The collimator holes may be of different dimensionsalong different axes, such as ellipse or rectangular shape holes, andthese holes may have cylindrical, conic or other converging or divergingshapes. In an alternative embodiment of the camera of the presentinvention, the camera is provided with a collimator having directionbias holes favoring detection from a predetermined lateral direction andlimiting detection from other directions.

[0061] As such, those skilled in the art to which the present inventionpertains can appreciate that while the present invention has beendescribed in terms of the above examples, the conception upon which thisdisclosure is based, may readily be utilized as a basis for thedesigning of other structures, methods and systems for carrying out thepurposes of the present invention.

[0062] It should be noted that the scope of the invention is not to beconstrued as limited by the illustrative examples set forth herein, butis to be determined in accordance with the appended claims.

1. A method of obtaining and reconstructing an image of a portion of abody, administered by radiopharmaceutical substance radiating gammarays, by using SPECT (single photon emission computerized tomography),for determination of functional information thereon, comprising thesteps of: (a) acquiring photons emitted from said portion of the body,by means of a detector capable of converting the photons into electricsignals, the detector having at least one crystal and adapted to detectemitted photons having incident angles in the range of 0 to more than 5degrees; (b) processing said electric signals by a position logiccircuitry and thereby transforming them into data indicative ofpositions on said photon detector crystal, where the photons haveimpinged the detector; and (c) reconstructing an image of a spatialdistribution of the pharmaceutical substance within the portion of thebody by processing said data and taking into consideration weightvalues, which are functions of either solid angles or solid angles anddistances between different discrete elements of the portion of the bodyand corresponding discrete elements of the projection of the portion ofthe body on the detector.
 2. The method of claim 1 wherein incidentangles of the detectable emitted photons are in the range of 0 to morethan 10 degrees.
 3. The method of claim 1 wherein incident angles of thedetectable emitted photons are in the range of 0 to about 90 degrees. 4.The method of claim 1 wherein said detector is a single photon detectorcrystal.
 5. The method of claim 1 wherein said detector is a photondetector crystal array comprising a plurality of single crystals.
 6. Themethod of claim 1 wherein said reconstructing an image by processingsaid data comprises the steps of: (a) dividing an area of the detectorfacing the body into M bins; (b) dividing the portion of the body into Nvoxels; (c) providing a set of values D_(i) (wherein i=1, . . . ,M)corresponding to the number of photons acquired by the i-th bin; (d)constructing a matrix P having matrix elements P_(ij) of weight valuesof the voxels of the portion of the body (wherein i=1, . . . ,M and j=1,. . . ,N), the matrix P setting a coupling between each bin of thedetector and each voxel of the portion of the body; (e) modeling arelation between said set of values D_(i) and a set of voxel valuesV_(j) of said image and deriving said set of voxel values V_(j) of saidimage, whereby said spatial distribution of the pharmaceutical substanceindicating the functional information on said portion of the body isobtained.
 7. The method of claim 6 wherein the step of modeling arelation between said set of values D_(i) and a set of voxel valuesV_(j) of said image and deriving said set of voxel values V_(j) of saidimage includes the step of solving a set of equations$D_{i} = {\sum\limits_{j = 1}^{N}\quad {P_{ij}V_{j}}}$

with respect to each value V_(j).
 8. The method of claim 6 wherein thestep of modeling a relation between said set of values D_(i) and a setof voxel values V_(j) of said image and deriving said set of voxelvalues V_(j) of said image includes the step of solving a set ofequations$D_{i} = {{\sum\limits_{j = 1}^{N}\quad {P_{ij}V_{j}}} + E_{i}}$

with respect to each value V_(j), wherein E_(i) is a set of measurementerrors.
 9. The method of claim 6 wherein the step of modeling a relationbetween said set of values D_(i) and a set of voxel values V_(j) of saidimage and deriving said set of voxel values V_(j) of said image includesthe step of solving an optimization problem for estimating the meanvalue λ(V_(j)) of the Poisson random variables V_(j), using the D_(i)values measured by the detector.
 10. The method of claim 9, whereinestimating the mean value λ(V_(j)) of the Poisson random variablesV_(j), is carried out by calculating the maximum of the likelihoodfunction${{L\left\lbrack {\lambda \left( D_{i} \right)} \right\rbrack} = {\prod\limits_{i = 1}^{M}\quad \frac{^{- {\lambda {(D_{i})}}}{\lambda \left( D_{i} \right)}^{D_{i}}}{D_{i}!}}},$

with respect to the unknowns V_(j).
 11. The method of claim 6 whereinthe step of modeling a relation between said set of values D_(i) and aset of voxel values V_(j) of said image and deriving said set of voxelvalues V_(j) of said image includes the step of solving a Bayesianoptimization problem utilizing a likelihood and penalty functions. 12.The method of claim 11, wherein the Bayesian optimization problem hasthe general form V=arg max{L[λ(D_(i))]+αF(V_(j),V_(k))}, where α is theweight that is given to the penalty function F
 13. The method of claim 6wherein the matrix P is a matrix in which each of the matrix elementsP_(ij) is a function of an average distance and solid angle at which adetector bin having an index i is viewed from the voxel having an indexj.
 14. The method of claim 6 wherein the matrix P is a matrix in whicheach of the matrix elements P_(ij) is a function of an average solidangle at which a detector bin having an index i is viewed from the voxelhaving an index j.
 15. The method of claim 6 wherein the matrix P is amatrix in which each of the matrix elements P_(ij) is a function of anaverage distance and solid angle at which a voxel having an index j isviewed from a detector bin having an index i.
 16. The method of claim 6wherein the matrix P is a matrix in which each of the matrix elementsP_(ij) is a function of an average solid angle at which a voxel havingan index j is viewed from a detector bin having an index i.
 17. Themethod of claim 6 wherein the matrix P is a matrix in which each of thematrix elements P_(ij) is a function of a solid angle and distance atwhich a detector bin having an index i is viewed from a center of avoxel having an index j.
 18. The method of claim 6 wherein the matrix Pis a matrix in which each of the matrix elements P_(ij) is a function ofa solid angle at which a detector bin having an index i is viewed from acenter of a voxel having an index j.
 19. The method of claim 6 whereinthe matrix P is a matrix in which each of the matrix elements is afunction of a solid angle and distance at which a center of a voxelhaving an index j is viewed from a detector bin having an index i. 20.The method of claim 6 wherein the matrix P is a matrix in which each ofthe matrix elements P_(ij) is a function of a solid angle at which acenter of a voxel having an index j is viewed from a detector bin havingan index i.
 21. The method of claim 6 wherein the modeling of therelation between said set of values D_(i) and a set of voxel valuesV_(j) of said image, includes the attenuation effect of the patientbody.
 22. The method of claim 21 wherein the matrix P is a matrix inwhich each of the matrix elements P_(ij) takes into account theattenuation density that exists on the path of the photons that emanateat voxel j and arrive at bin i, for each detector position k.
 23. Themethod of claim 21 wherein the matrix P is a matrix in which each of thematrix elements P_(ij) takes into account the attenuation density thatexists on the path of the photons that emanate at voxel j and arrive atbin i, for each detector position k and for each energy peak of theradio-pharmaceutical substance that is used.
 24. The method of claim 6wherein the matrix P is a matrix in which each of the matrix elementsP_(ij) is multiplied by the relative effective area of bin i associatedwith the solid angle between voxel j and bin I, when collimators areused.
 25. The method of claim 1 wherein said detector is adapted torotate around the body.
 26. The method of claim 1 wherein said detectoris adapted to move relative to the body.
 27. The method of claim 1wherein said detector is a crystal detector array surrounding saidportion of the body, the array comprising at least one row of aplurality of said photon detector crystals.
 28. The method of claim 1wherein said detector is placed in proximity of said portion of thebody, while the body is rotated around a fixed axis.
 29. The method ofclaim 1 wherein said at least one crystal is a crystal utilizing atleast one photo-multiplier for converting photons into electric signals.30. The method of claim 29 wherein said at least one crystal is acrystal selected from the group consisting of Sodium Iodine (NaI),Bismuth Germnanate (BGO), Yttrium Oxyorthosilicate (YSO), Cerium-dopedLutetium Oxyorthosilicate (LSO) and Cesium-Iodine (CsI).
 31. The methodof claim 1 wherein said at least one crystal is a semiconductor crystal.32. The method of claim 31 wherein said semiconductor crystal is acrystal selected from the group consisting of Cadmium-Telluride (CdTe),Cadmium-Zinc-Telluride (CeZnTe) and Lead Iodine (PbI).
 33. The method ofclaim 1 wherein said detector is of the kind used in an Anger camera.34. The method of claim 1 wherein said detector includes at least a pairof septa mounted along an axis of the detector, the septa provided forlimiting the field of view.
 35. A SPECT apparatus for obtaining andreconstructing an image of a 25 portion of a body administered by aradiopharmaceutical substance for the determination of functionalinformation thereon, comprising: (a) a detector adapted to detectphotons emitted from said portion of the body having incident angles inthe range of 0 to more than 5 degrees, said detector having at least onephoton detector crystal, the detector adapted to convert photons intoelectric signals; (b) a position logic circuitry for processing saidelectric signals and thereby transforming them into data indicative ofpositions on said photon detector crystal, where the photons haveimpinged the detector; and (c) a data analysis processor forreconstructing an image of a spatial distribution of the pharmaceuticalsubstance within said portion of the body by processing said data andtaking into consideration weight values which are functions of solidangles between discrete elements of the portion of the body andcorresponding elements of said portion's projection on the detector. 36.The apparatus of claim 35, wherein the detector is provided with acollimator adapted to allow emitted photons having incident angles inthe range of 0 to more than 5 degrees to reach the detector.
 37. Theapparatus of claim 35 wherein the detector is provided with a collimatoradapted to allow emitted photons having incident angles in the range of0 to more than 10 degrees to reach the detector.
 38. The apparatus ofclaim 35 wherein the detector does not include a collimator, and isadapted to detect emitted photons having incident angles in the range of0 to about 90 degrees.
 39. The apparatus of claim 35 wherein saiddetector is a single photon detector crystal.
 40. The apparatus of claim35 wherein said detector comprises a photon detector crystal arraycomprising a plurality of single crystals.
 41. The apparatus of claim 35wherein said detector is adapted to rotate around the body.
 42. Theapparatus of claim 35 wherein said detector is adapted to move relativeto the body.
 43. The apparatus of claim 35 wherein said detector is acrystal detector array surrounding said portion of the body, the arraycomprising at least one row of a plurality of said photon detectorcrystals.
 44. The apparatus of claim 35 wherein said detector is static,while the body is rotated around a fixed axis.
 45. The apparatus ofclaim 35 wherein said at least one crystal is a crystal utilizing atleast one photo-multiplier for converting photons into electric signals.46. The apparatus of claim 45 wherein said at least one crystal is acrystal selected from the group consisting of Sodium Iodine (NaI),Bismuth Germanate (BGO), Yttrium Oxyorthosilicate (YSO), Cerium-dopedLutetium Oxyorthosilicate (LSO) and Cesium-Iodine (CsI).
 47. Theapparatus of claim 35 wherein said at least one crystal is asemiconductor crystal.
 48. The apparatus of claim 47 wherein saidsemiconductor crystal is a crystal selected from the group consisting ofCadmium-Telluride (CdTe), Cadmium-Zinc-Telluride (CeZnTe) and LeadIodine (PbI).
 49. The apparatus of claim 35 wherein said detector is ofthe kind used in an Anger camera.
 50. The apparatus of claim 35 whereinsaid detector includes at least a pair of septa mounted along an axis ofthe detector, the septa provided for limiting the field of view.
 51. Theapparatus of claim 35, wherein the detector is provided with acollimator having holes that are symmetric, such as circular, square orhexagonal shaped holes.
 52. The apparatus of claim 35, wherein thedetector is provided with a collimator having direction bias holesfavoring detection from a predetermined lateral direction and limitingdetection from other directions.
 53. The apparatus of claim 35, whereinthe detector is provided with a collimator having non-symmetric holes.54. The apparatus of claim 35, wherein the detector is provided with acollimator having holes of different dimensions along different axes,such as ellipse or rectangular shape holes.
 55. The apparatus of claim35, wherein the detector is provided with a collimator having bores ofcylindrical, conic or other converging or diverging shapes.
 56. A methodof obtaining and reconstructing an image of a portion of a body,administered by radiopharmaceutical substance radiating gamma rays, byusing SPECT (single photon emission computerized tomography), fordetermination of functional information thereon, substantially asdescribed in the aforementioned specification and accompanying figures.57. A SPECT apparatus for obtaining and reconstructing an image of aportion of a body administered by a radiopharmaceutical substance forthe determination of functional information thereon, substantially asdescribed in the aforementioned specification and accompanying figures.